Ulysses' trip

Latest post

May 14, 2025, 14:58:53

After using computers for all so many years, for the first time, the Insert key was actually useful when I was editing a file. I always thought the only reason it exists is for causing small headaches when my dumb fingers accidentally touch it.

The key was used when I was editing a string in a binary file, and I wanted to make sure that the offsets of all the contents afterward were not affected.

Articles

Feb 3, 2023
Introducing bra–ket notation to math learners

Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you.
- Categories: math
- Tags: from zhihu, quantum mechanics
Feb 2, 2023
Even solutions to bound states in an odd number of $\delta$ potential wells

We try solving the even function solutions to the time-independent Schrödinger equation for the potential $V=-\alpha\sum_{j=-n}^n\delta(x-ja)$ such that $E<0$ (bound states).
- Categories: physics
- Tags: from zhihu, quantum mechanics
Feb 1, 2023
Defend our earth against aliens’ bullets!

The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.
- Categories: physics
- Tags: calculus, classical mechanics, kepler problem, from zhihu
Jan 18, 2023
This is what will happen after you get a haircut

Denote the length distribution of one’s hair to be $f(l,t)$ , where $l$ is hair length, and $t$ is time. Considering that each hair may be lost naturally from time to time (there is a probability of $\lambda\,\mathrm dt$ for each hair to be lost within time range from $t$ to $t+\mathrm dt$ ) and then restart growing from zero length, how will the length distribution of hair evolve with time? It turns out that we may model it with a first-order PDE.
- Categories: math
- Tags: calculus, probability, pde
Jan 11, 2023
I want to invent a better way to read numbers

Reading numbers in English is a pain. I want to invent a better way to read numbers!
- Categories: language
- Tags: imagination
Dec 25, 2022
The longest all- $1$ substring of a random bit string

Given your probability of breaking the combo at each note, what is the probability distribution of your max combo in the rhythm game chart? I considered the problem seriously!
- Categories: math
- Tags: long paper, rhythm game, algorithm, probability
Dec 5, 2022
I made this, for the number of days in a week is prime

The number of days in a week is prime, so we cannot utilize weekly periods to help us remember periodical events unless the period is a multiple of 7. However, there may be something that we need to get reminded of which happens once per two days or three days. For example, I wash my hair once per two days and wash my clothes once per eight days. To solve the problem, I wrote a Ruby program to help remind me of those routines.
- Categories: programming
- Tags: selfhosting, linux, ruby
Nov 28, 2022
Using ntfy to warn me when my computer is discharging

I use udev and systemd to send a notification to my phone via ntfy automatically whenever my laptop is discharging.
- Categories: programming
- Tags: selfhosting, linux
Nov 20, 2022
How to construct mechanics in higher dimensions?

We can derive the equation of motion for mechanical systems in a Galileo universe with $\iota$ time dimensions and $\chi$ space dimensions by generalizing the principle of relativity and Hamilton’s principle.
- Categories: physics
- Tags: from zhihu, classical mechanics, imagination
Nov 18, 2022
When a supersonic airplane flies over your head

Suppose a supersonic airplane has Mach number $M$ . It flies horizontally. At some time, it flies past over your head at height $h$ . Then, the distance between you and it when you have just heard it is $Mh$ .
- Categories: physics
- Tags: from zhihu